Francis Edward Su
My Ph.D. research was in probability--- specifically the study of rates of convergence of random walks on groups and homogeneous spaces (spaces on which groups act). I have been advocating the use of the discrepancy metric (instead of the total variation metric) for random walks on continuous state spaces. Discrepancy is a notion (borrowed from number theorists) of how uniformly distributed a sequence can be, and can be used to define a metric on probabilities. I have been working to develop effective bounds for this metric. A class of random walks that I have studied in detail are random walk on the circle generated by irrational rotations. This leads to some interesting diophantine analysis and continued fraction results that affect the rate of convergence of such walks.
My interest in "fair division" problems began in graduate school. A prototypical example is the classical question due to Steinhaus of "how to cut a cake fairly". As an undergraduate I learned a lot of combinatorial topology and studied some of its applications to fixed point theory. In graduate school I realized that such ideas could form the basis of a new approach to fair division problems in game theory. Since then I've become interested in other aspects of game theory, and am collaborating with some economists on developing practical procedures for fair division and resource allocation.
In recent years, I've become interested in triangulations of objects (of the kind that often appear in fair division problems). Often these are manifolds or branched manifolds of various kinds. Thus my interest in economic questions has stimulated my interest in geometric combinatorics and discrete geometry. I have a particular interest in the development of combinatorial fixed point theorems.
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Last modified: December, 1999